Problem: The following line passes through point $(4, 10)$ : $y = \dfrac{9}{13} x + b$ What is the value of the $y$ -intercept $b$ ?
Substituting $(4, 10)$ into the equation gives: $10 = \dfrac{9}{13} \cdot 4 + b$ $10 = \dfrac{36}{13} + b$ $b = 10 - \dfrac{36}{13}$ $b = \dfrac{94}{13}$ Plugging in $\dfrac{94}{13}$ for $b$, we get $y = \dfrac{9}{13} x + \dfrac{94}{13}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${11}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${\llap{-}11}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${11}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${\llap{-}11}$ $(4, 10)$